An Efficient Scheme for Sampling in Constrained Domains

TL;DR

This paper introduces an efficient sampling method using inversion in a sphere within the Metropolis-Hastings framework to handle constrained domains like simplices, spheres, and hypercubes, improving sampling efficiency.

Contribution

It presents a novel transformation-based sampling scheme that simplifies constrained domain sampling within the Metropolis-Hastings algorithm.

Findings

Effective sampling in constrained domains demonstrated.

Superior performance compared to existing methods.

Applicable to various geometric constraints.

Abstract

The creation of optimal samplers can be a challenging task, especially in the presence of constraints on the support of parameters. One way of mitigating the severity of this challenge is to work with transformed variables, where the support is more conducive to sampling. In this work, a particular transformation called inversion in a sphere is embedded within the popular Metropolis-Hastings paradigm to effectively sample in such scenarios. The method is illustrated on three domains: the standard simplex (sum-to-one constraint), a sector of an $n$-sphere, and hypercubes. The method's performance is assessed using simulation studies with comparisons to strategies from existing literature.